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This research focuses on the stochastic functional differential equations driven by G-Brownian motion (G-SFDEs) with infinite delay. It is proved that the trivial solution of a G-SFDE with infinite delay is exponentially stable in mean square. An example is also presented to illustrate the effectiveness of the obtained theory.

This study is concerned with the stabilization analysis and controller design for networked systems with stochastic sampling and two‐channel deception attacks. First, we give a general matrix decomposition approach which is applicable to scenarios where the system matrix A$A$ contains complex‐value eigenvalues. Then, a discrete stochastic framework is established for a class of networked systems which considers the joint effects of sampling errors and two‐channel deception attacks. Utilizing the matrix decomposition approach introduced in this study, it becomes feasible to decouple the expectation operations for specific coupling matrices characterized by substantial nonlinearity and randomness. Based on this, a stabilization controller is constructed that ensures the exponential mean‐square stability of the resulting discrete stochastic system. Finally, three simulation examples are provided to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this brief note, a probability theory approach is proposed to investigate the stability analysis issue for a class of networked sampled-data systems with packet dropouts. The continuous-time linear system under consideration is first transformed into a discrete-time system, where the system matrix of the discrete-time system is characterized by stochastic characteristic. Then, by the matrix exponential computation, an equivalent discrete-time stochastic system is established. Based on this, a controller is designed by the law of total expectation, which guarantees the stochastic stability of the closed-loop stochastic system. Finally, a numerical example and an example using power grid with IEEE 4-bus line are used to verify the effectiveness and applicability of the proposed design algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method. [ABSTRACT FROM AUTHOR]

Event-triggered schemes are characterized in less communication traffic while maintaining the resulting controlled plant’s desired stability and performance criteria. In the presence of packet dropouts, this paper is concerned with the modeling and control problems for a class of discrete-time stochastic systems with event-triggered schemes. Two different mathematical analysis methods are proposed to model the packet loss when an event-triggered scheme is subject to packet loss. First, a stochastic distributed sequence satisfying the Bernoulli process is utilized to model the triggered packets transmitted in the communication networks. Considering the difference between time-triggered and event-triggered schemes, an equivalent model with a random sequence not satisfying a Bernoulli distribution process is also analyzed, which is not the same as some existing results in the literature. Then, the mean-square exponential stability of resulting augmented system is guaranteed and the prescribed ${H}_{\infty }$ performance level is achieved by solving resulting discrete ${P}$ -problem. Two examples with simulations are provided to validate the analytical results and demonstrate the effectiveness of the proposed co-design techniques. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the modeling and stabilization problems for a class of discrete-time stochastic networked systems (DSNSs) subject to successive packet losses. The system under consideration is transformed into a stochastic one with bounded stochastic delay. Considering that the stochastic delay is characterized by nonuniform distribution, a new equivalent model is then constructed that enables the DSNS’s controller design to benefit from knowing the probability characteristic of packet losses. Specially, to verify this feature, the probabilities of the delay can be explicitly obtained by utilizing the formula of total probability, which is critical to model transformation and analyze practical problems that exist in DSNSs. Based on the proposed model, sufficient conditions are established under which the globally mean-square asymptotic stability of resulting stochastic delay closed-loop system is guaranteed, and a delay-distribution-dependent design procedure is then proposed. A numerical example with simulation is provided to validate the analytical results and demonstrate the effectiveness of the design procedure. [ABSTRACT FROM AUTHOR]

This paper considers the sample-data-based consensus problem of multiagent systems with time-varying delay and packet losses. To distinguish the time delays caused by network-induced time-delay and packet losses, the switched system is utilized. A lower gain controller is designed based on the solution of a parametric algebraic Riccati equation. The Lyapunov stability theory is utilized to obtain the limitations on the frequency and the duration of packet losses which guarantees the consensus of multiagent systems. On the other hand, we theoretically prove that refined time-delay function can reduce the conservatism. A simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the stochastic analysis and H ∞ controller design problems of networked systems with packet dropouts and false data injection attacks are investigated. Different from the existing literature, we focus on the linear networked systems with external disturbances and both sensor-controller channel and controller-actuator channel are studied. First, we present a discrete-time modeling framework that leads to a stochastic closed-loop system with randomly varying parameters. To facilitate the analysis and H ∞ control of resulting discrete-time stochastic closed-loop system, an equivalent yet analyzable stochastic augmented model is further constructed by matrix exponential computation. Based on this model, a stability condition is derived in the form of linear matrix inequality (LMI) with the aid of a reduced-order confluent Vandermonde matrix, Kronecker product operation, and law of total expectation. Specifically, the dimension of the LMI obtained in this article does not increase as the upper bound of consecutive packet dropouts does, which is also different from the existing literature. Subsequently, a desired H ∞ controller is obtained such that the original discrete-time stochastic closed-loop system is exponentially mean-square stable with a prescribed H ∞ performance. Finally, a numerical example and a direct current motor system are exploited to substantiate the effectiveness and practicability of the designed strategy.

This article addresses the issue of output-feedback consensus control of multiagent systems under the directed topology and subject to bounded external disturbances. By employing a smooth time-varying function, a distributed practical predefined-time (PPT) observer is developed to estimate the reference trajectory for the entire team (i.e., the leader's state) and a practical preset-time extended-state observer is also proposed to estimate bounded disturbances and unmeasurable system states. Next, a novel continuous and nonsingular PPT consensus control law is designed on the basis of the observers. Furthermore, the designed control protocol can achieve PPT stability, that is, consensus tracking errors are enforced to a neighborhood around zero within a predetermined time, which can be specified a priori, independent of initial states of agents and/or any other design parameters. Finally, illustrative numerical examples, including a comparative one, are provided to demonstrate the performance of the present predefined-time control approach.

This article focuses on the sampled-data synchronization issue for a class of complex dynamical networks (CDNs) subject to noisy sampling intervals and successive packet losses. The sampling intervals are subject to noisy perturbations, and categorical distribution is used to characterize the sampling errors of noisy sampling intervals. By means of the input delay approach, the CDN under consideration is first converted into a delay system with delayed input subject to dual randomness and probability distribution characteristic. To verify the probability distribution characteristic of the delayed input, a novel characterization method is proposed, which is not the same as that of some existing literature. Based on this, a unified framework is then established. By recurring to the techniques of stochastic analysis, a probability-distribution-dependent controller is designed to guarantee the mean-square exponential synchronization of the error dynamical network. Subsequently, a special model is considered where only the lower and upper bounds of delayed input are utilized. Finally, to verify the analysis results and testify the effectiveness and superiority of the designed synchronization algorithm, a numerical example and an example using Chua's circuit are given.